Steady-state solutions for strongly exothermic ignition in symmetric geometries

We consider the steady-state solutions for the strongly exothermicdecomposition of a combustible material under Arrhenius kineticsin symmetric geometries, neglecting the consumption of the material. We solve the nonlinear boundary-value problem forthe dimensionless temperature, u, + + H(u)e^–1/u= 0, subject to du/dr = 0at r = 0, and Bi(u_a– u) = du/dratr = 1, for >> 1, using both numerical and asymptoticmethods. All of the features of the bifurcation diagram andthe steady-state solutions that we determine numerically, includingmultiplicity of steady-state solutions and the existence incertain cases of a boundary layer at the centre of the material,can be explained using asymptotic techniques. Received 30 April, 1999. Revised 29 February, 2000. Accepted 29 February, 2000.     

Designing polymer additives to minimise loss

The solubility of additives in polymers is shown to determine the state of the additive in a processed sample and the mechanisms by which it may be lost. The loss of additives is described in terms of a model which considers the effects of solubility, diffusion rate and volatility, and it is shown that the rate and mechanism of loss depends upon these quantities and upon the sample geometry. The effects of additive structure on loss mechanism and rate are discussed and the implications for additive design are reviewed.     

Chemical clock reactions: The effect of precursor consumption

During a clock reaction an initial induction period is observed before a significant change in concentration of one of the chemical species occurs. In this study we develop the results of Billingham and Needham (1993) who studied a particular class of inhibited autocatalytic clock reactions. We obtain modified expressions for the length of the induction period and show that characteristic clock reaction behaviour is only observed within certain parameter limits. This revised version was published online in July 2006 with corrections to the Cover Date.     

The application of simultaneous chemiluminescence and thermal analysis for studying the glass transition and oxidative stability of poly(N-vinyl-2-pyrrolidone)

A computer-controlled chemiluminescence (CL) instrument incorporating a differential scanning calorimeter was used to simultaneously acquire photochemical and enthalpic data for poly(N-vinyl-2-pyrrolidone) (PVP). Samples were subjected to a linear temperature ramp under nitrogen and their luminescence response recorded. The resultant dynamic CL peak is attributable to the decomposition of hydroperoxide groups and the subsequent mutual termination of secondary polymer peroxyl radicals. It is shown that dynamic CL can be used to characterize the level of oxidation in PVP, which in commercial samples, may be partly related to the level of residual polymerization inititor and to the drying process. The temperature at which maximum CL emission occurs correlates with the glass transition temperature (T_g) of the polymer and increases with increasing molecular weight. A marked increase in the T_g of PVP occurs after it is aged in air for 24 h at 120°C. This is due to the loss of adsorbed moisture from the polymer which was confirmed by thermogravimetric analysis. Oxidation profiles of PVP were obtained by plotting the integrated CL peak area as a function of aging time. The profiles are compared with data obtained from isothermal CL and viscosity measurements. Gas perturbation experiments suggest that when drying PVP under nitrogen at elevated temperatures significant populations of longlived macroalkyl radicals are formed which can peroxidize the polymer on exposure to air. © 1993 John Wiley & Sons, Inc.     

Gravity-driven thin-film flow using a new contact line model

In this paper, we consider how a new model for the motion ofa contact line, proposed by Shikhmurzaev (1993, Int. J. MultiphaseFlow, 19, 589-–610), affects predictions for the gravity-drivenflow of a thin film down an inclined plane. We find that forsufficiently thin films, the model reduces to Navier slip withthe contact angle equal to its static value, while for thickerfilms the model has a character of its own, with a slip regionthat becomes larger, the thicker the film and a contact anglethat increases as the thickness of the film increases.     

Stabiliser partitioning and oxidative degradation in rubber-toughened polypropylene

Solubility measurements on an antioxidant and a UV stabiliser in polypropylene and an ethylene/propylene rubber are correlated with partitioning between the two bulk polymers and between the phases of a blend. At low concentrations, partitioning concentrates the additive in the rubber; the effect increases with temperature, so that most of the additive will be in this phase at processing temperatures. Calculations suggest that the additives can diffuse between phases fast enough to compensate for consumption in either at service temperatures. At processing temperatures, diffusion of antioxidant from the more stable rubber phase to the polypropylene phase may be slow enough to limit protection from oxidation.     

ABC triblock polymethacrylates: Group transfer polymerization synthesis of the ABC,ACB, and BAC topological isomers and solution characterization

ABC triblock copolymers of methyl methacrylate (MMA), (dimethylamino)-ethyl methacrylate (DMAEMA), and tetrahydropyranyl methacrylate (THPMA) consisting of 12 units of each type of monomer were synthesized by group transfer polymerization (GTP). These were the three topological isomers with differentblock sequences: DMAEMA₁₂-THPMA₁₂-MMA₁₂, DMAEMA₁₂-MMA₁₂-THPMA₁₂, and THPMA₁₂-DMAEMA₁₂-MMA₁₂. The molecular weights and molecular weight distributions of the copolymers were determined by gel permeation chromatography (GPC) in tetrahydrofuran, and their number-average degrees of polymerization and copolymer compositions were calculated by proton nuclear magnetic resonance spectroscopy (¹H-NMR). These molecular weights and degrees of polymerization corresponded closely to the values expected from the monomer/initiator ratios. The polydispersities were low as expected for GTP, and ranged from 1.09 to 1.25. The three triblocks were chemically modified by converting the THPMA units to methacrylic acid (MAA) units either by thermolysis or acid hydrolysis. The resulting ABC triblock poly-ampholytes were characterized by ¹H-NMR spectroscopy and hydrogen ion titration. Aqueous GPC studies in 1.0M NaCl at pH 8.5 showed that the triblock copolymers form micelles whose size depends on their block sequence. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 617–631, 1998